convection-enhanced delivery of therapeutics for brain …...r. raghavan, et al. 2 neurosurg. focus...

OTIVATED in part by the profound difficulties as-sociated with improving treatment for glio-blastoma multiforme, many people have been

exploring positive-pressure infusion as a means of de-livering therapeutic agents into the brain. Pioneered byresearchers at the NIH in the US,22,27,28 CED of an agentthrough the interstitial space provides a means of achiev-ing therapeutic drug concentrations within the parenchy-mal tissues on a regional basis, without the limitationsimposed on delivery by the BBB. In the prototypical ver-sion of such an approach, one or more catheters are im-planted into the brain under image guidance, an infusionpump is connected to the catheter(s) to drive the flow, andthe agent is then pumped directly into the target tissues,which dilate in response to the pressure field and allowpermeation of the agent (Fig. 1).

A potential advantage of this method is the ability of theagent to reach cells that have invaded the peritumoral re-gion and beyond, and thus making it arguably possibleto offer hope of significantly reducing (if not halting) thespread of the disease. A number of clinical centers arenow involved in instrumentation and imaging develop-ment, testing of experimental protocols, and clinical trialsof the technique in humans in the hopes of bringing theprocedure into routine clinical use (for example, see thereview by Broaddus and colleagues5). For large moleculeshaving a 50,000-D or greater mass, the diffusive spreadwill often extend less than 1 mm in a day, and only as largeas that if metabolic and other loss mechanisms do notflush it from the parenchyma. The flow of such a fluid co-injected with a drug can carry such molecules much far-ther, however, and in certain idealized scenarios can fillthe intervening region with a full concentration of drugper unit of available volume. (Diffusive spread, of course,results in exponentially decreasing concentrations awayfrom a source.)

Nonetheless, the success of these attempts has to datebeen limited given the lack of appropriate planning, guid-ance, and infusion technologies. Currently, intraparenchy-

Neurosurg. Focus / Volume 20 / April, 2006

Neurosurg Focus 20 (3):E12, 2006

Convection-enhanced delivery of therapeutics for braindisease, and its optimization

RAGHU RAGHAVAN, PH.D., MARTIN L. BRADY, PH.D.,MARÍA INMACULADA RODRÍGUEZ-PONCE, PH.D., ANDREAS HARTLEP, PH.D.,CHRISTOPH PEDAIN, PH.D., AND JOHN H. SAMPSON, M.D., PH.D.

Therataxis, LLC, Baltimore, Maryland; BrainLAB AG, Heimstetten, Germany; Division ofNeurosurgery, Department of Surgery; and Department of Pathology, Duke University MedicalCenter, Durham, North Carolina

ü Convection-enhanced delivery (CED) is the continuous injection under positive pressure of a fluid containing a ther-apeutic agent. This technique was proposed and introduced by researchers from the US National Institutes of Health(NIH) by the early 1990s to deliver drugs that would otherwise not cross the blood–brain barrier into the parenchymaand that would be too large to diffuse effectively over the required distances were they simply deposited into the tis-sue. Despite the many years that have elapsed, this technique remains experimental because of both the absence ofapproved drugs for intraparenchymal delivery and the difficulty of guaranteed delivery to delineated regions of thebrain. During the first decade after the NIH researchers founded this analytical model of drug distribution, the resultsof several computer simulations that had been conducted according to more realistic assumptions were also published,revealing encouraging results. In the late 1990s, one of the authors of the present paper proposed the development ofa computer model that would predict the distribution specific to a particular patient (brain) based on obtainable datafrom radiological images. Several key developments in imaging technology and, in particular, the relationships be-tween image-obtained quantities and other parameters that enter models of the CED process have been required to im-plement this model. Note that delivery devices need further development.

In the present paper we review key features of CED as well as modeling of the procedure and indulge in informedspeculation on optimizing the direct delivery of therapeutic agents into brain tissue.

KEY WORDS • convection-enhanced delivery • brain • computer simulation •drug delivery system

M

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Abbreviations used in this paper: BBB = blood–brain barrier;CED = convection-enhanced delivery; CSF = cerebrospinal fluid;CT = computerized tomography; DTPA = diethylenetriamine pen-taacetic acid; IFP = interstitial fluid pressure; MR = magnetic reso-nance; NIH = National Institutes of Health; SPECT = single-photonemission computerized tomography.

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mally injected agents are not monitored to determine theirspatial disposition in tissue. Following CED of novel ther-apeutic agents in humans with malignant gliomas, we havebeen able to obtain images documenting the spatial distri-bution of large molecules in several patients with brain tu-mors (JH Sampson, et al., unpublished data). These datademonstrate that CED is capable of significantly enhanc-ing the spatial distribution of drugs beyond what is possi-ble with diffusion alone. In our initial studies, the measuredspatial distributions varied significantly from patient topatient in an apparently unpredictable fashion. Thus, not-withstanding improvements in drug distributions, the ac-tual geometry of the spatial distribution in a given patientfrequently failed to reach the intended regions of interestand left regions of likely tumor recurrence unaddressed.This variability clearly constrains the potential efficacy ofthe therapeutic agent being delivered.

Therefore we see that an important issue associatedwith the development of CED lay in understanding howthe spread of an agent within the brain might deviate froman ideally sought volume of distribution. In the next sec-tion, we provide an overview of the various factors affect-ing the spread of an infused volume. This topic naturallyleads into how we may mitigate the deleterious effects ofsome of these phenomena, and we discuss some aspects ofthe delivery catheters in the subsequent section. Resumingour main theme of understanding CED, we then discusshow we may model the effect of the various factors and,importantly, how we may obtain the constitutive proper-ties of the tissue and other parameters on which the modeldepends. Validating such models or, indeed, understand-ing drug distribution requires us, in the final analysis, totrack infused agents and obtain data. We devote a briefsection to the use of MR imaging markers. Althoughmarkers for other imaging modalities (CT, SPECT, pos-itron emission tomography, and so forth) are potentiallyimportant, we have had limited experience with these—except for SPECT, which we do discuss. We concludewith our hopes for the near future: optimizing CED forbrain therapeutics, particularly for brain cancer. Note thatour opinions are confined to issues of increasing the effi-cacy of CED; we do not compare it with other delivery

methods,8 nor do we address the development of drugs re-quiring or significantly benefiting from direct intraparen-chymal delivery.

Factors Affecting Drug Distribution by CED

In most procedures for intraparenchymal infusion or in-jection, the delivery device is stereotactically guided to itsintracranial target through a bur hole. For slow infusionprocesses (in humans, typically , 0.3 ml/hour), the cathe-ter might be left indwelling for several days. ConventionalMR imaging or CT scanning studies are typically usedpreoperatively to estimate the optimal insertion trajectory.However, the final details of the implantation procedureare usually specific to the design of the delivery device,the rate at which the infusion or injection is to occur, andthe number of devices that must be inserted and/or passesthat must be made to obtain adequate therapeutic coverageof the targeted volume. Infusion methodologies for bothframed and frameless stereotaxy have been developed,with forms for the latter being optimized for use in the in-terventional MR imaging context.

Key features affecting the distribution of molecular so-lutions when pumped into brain parenchyma are summa-rized in Fig. 2.6–8,10 Once the pump parameters (flow rateand duration) have been set, the fluid flow in the poroelas-tic medium of the brain parenchyma acts as the primarycarrier of large-molecule drugs. The interstitial pathwaysin the brain29,30 allow such convective transport inde-pendent of the molecule size, for a range of sizes.11 Ofcourse, factors such as lipophilicity can affect the transport;for water-soluble proteins, however, convective transportdominates at least for short times. The flow of fluid inthe brain is quite tortuous, and the distribution of drug mol-ecules, even for convective transport, exhibits what isknown as “hydrodynamic dispersion”1,4—namely, a seem-ingly diffusive spread given the tortuosity of the paths,with apparent diffusivity being related to the speed of con-vective flow. Furthermore, various barriers including thepial surfaces of the cortex limit convective transport of thedrug. Over longer time periods, diffusion (random move-ment of the molecules within the extracellular spaces of theinterstitium), loss through the capillaries, and, of course,drug action (metabolism) determine the distribution pat-terns of the drug. These processes are represented in Fig. 3,which shows the results of a 90-minute infusion into a pigbrain (Fig. 3b) followed by imaging 20 hours thereafter(Fig. 3c). These data were obtained from an experimentdirected by Michael Moseley at Stanford University, Stan-ford, California, and funded by what was then Image-Guided Neurologics, Inc.

Before the fundamental mechanisms of transport andmetabolic action take place, however, several issues mustbe overcome or avoided: tissue damage on catheter in-sertion, ever-present air bubbles that, if not properly ad-dressed, can provide unpredictable paths for subsequentfluid flow, and so forth. We have attempted to list suchfactors in Table 1 and describe them in more detail in thetext.

Tissue Damage and Reflux

One important phenomenon during infusion is back-

R. Raghavan, et al.

2 Neurosurg. Focus / Volume 20 / April, 2006

FIG. 1. Schematic showing concentration profiles for pressure-driven and diffusion-driven deliveries. Compared with diffusion-driven delivery, the pressure-driven delivery results in a higherconcentration extending farther from the delivery site.


http://www.aans.org/education/journal/neurosurgical/apr06/20-4-12f1.html

flow of the infused agent along the catheter’s insertiontrack, which can happen for one of two reasons. First, andmost obvious, backflow can occur if the catheter has me-chanically disrupted the tissue enough to allow a void toform around its outer wall. In such cases, the infused agentsimply refluxes through that gap with relatively little pres-sure-driven flow into the target tissues. It seems obvious,and the point has been confirmed in at least one careful-ly performed study,11 that soft catheters are less likely tocause mechanical disruption. In particular, surgeons rou-tinely see brain shifts during craniotomies, requiring themmentally to adjust the image guidance system for propercatheter positioning during postoperative infusions. Re-ported data confirm that soft catheters can move with thebrain shift and cause less disruption and breaking of seals,thereby preventing this form of backflow. The more in-trinsic reason for backflow is described next.

Transient and Steady-State Characteristics: IntrinsicBackflow

Even when no void has formed during catheter inser-tion or when the tissue has sealed against the outer wall, asecond type of backflow can occur. During this intrinsicbackflow, pressure associated with the infusion process

pushes against the tissues and causes them to separateminutely from the catheter, until the shear forces in the tis-sue balance the pressure field and the retrograde axialflow stops (Fig. 4). To our knowledge, intrinsic backflowwas first described by Morrison and colleagues.26

The predictions or theories of backflow have been basedon steady-state considerations and depend on the assump-tion that the backflow is fully developed before the fluidhas spread significantly into tissue. The basic mathematicsof poroelasticity reveals that the pressure is diffusive andthus does not reach a constant value in a finite amountof time. Therefore, the experimental conditions in whichbackflow predictions can be validated are particular, re-quiring relatively small-diameter catheters and strong re-sistance to spread in the tissue or tissue easily deformed byfluid pressure or both. An initial detailed experimentalstudy has been conducted and its data reveal many inter-esting effects of pressure disequilibration that make theaccurate quantitative prediction of backflow difficult (ZJChen, et al., unpublished data).

Nevertheless, certain facts remain: backflow can occur,allows fluid to flow back along the catheter track for sev-eral centimeters for a catheter having an outer diameterof 1 mm, and must be taken into account. Such backflowcan lead to spreading of the agent into regions of the brain


Convection-enhanced delivery and optimization

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FIG. 2. Diagram depicting a possible subdivision of the problem involved in CED. The distribution can be inferredfrom knowledge about influx, transport, and efflux parameters.

FIG. 3. a: Sketch illustrating an infusion catheter in tissue (not to scale). Orange elongated cells represent white mat-ter tracts. The fluid infused from the catheter forms a small annulus around the outside of the catheter, the backflow. Thiscylinder is the source of the subsequent infusion, which preferentially follows the white matter tracts. b: A T1-weight-ed MR image demonstrating the infusion of Gd-DTPA into a pig brain. The infusion pattern has an irregular shape, pref-erentially following the white matter tracts. The image was acquired at the end of the infusion. c: A T1-weighted MRimage obtained 1 day after the infusion was finished, depicting the effects from the same infusion shown in panel b. TheGd-DTPA has diffused to distances far beyond the original volume shown in panel b.




where it is not intended and, possibly, in a diminution ofthe dose otherwise needed within the target tissues. (Thesame principle, of course, holds for reflux during catheterwithdrawal.) The problem could be particularly acute incortical infusions, when backflow of the agent along theinsertion track and into the subarachnoid space might oc-cur, with subsequent widespread distribution of the agentby the circulating CSF. A model of the mechanics of thebackflow process indicates that the backflow distance (fora fixed rate of fluid delivery through the catheter) variesas the four-fifths power of the outer radius of the catheter.Thus, other things being equal, the use of a thin catheter isadvantageous, as proven by other researchers,22 and thedifficulty in placing a very thin catheter due to its floppi-ness can be overcome by having a “step design”20 in whichthe thinner catheter protrudes for a short length beyond amore rigid and wider cannula. The thinness will preventbackflow beyond the protruding length for sufficiently

small infusion rates. Current clinical trials, however, in-volve the catheters with outer diameters of 1 mm (the in-fusion catheter in the step design20 was 168 mm). In test-ing the model compared with observations of infusions,predicted backflow distances on the order of 20 mm wereindeed found to occur. As a result of these studies, somenavigation systems come with guidelines, recommendedby us, for catheter placement for infusions in humans toavoid backflow into cavities that would compromise theinfusion. We quote from those offered by BrainLAB AG(catheter package insert)

1. Depth Line, which displays a cylinder along the cathetertrajectory representing a recommended zone within which thecatheter should not cross any pial surfaces. This line must becomputed dynamically based on at least flow rate and cathetersize. Further the depth line should show a sphere around thecatheter tip representing a recommended distance to fluid filledcavities.

2. Distance Line, which displays a sphere of 2 cm diameteraround the catheter tip representing the recommended minimaldistance between catheters. The outer circle gives the DistanceLine and the inner circle in combination with the cylinder alongthe trajectory the Depth Line.

Refer to Fig. 5 for additional information.An example of the need for such guidelines is repre-

sented in Fig. 6, which illustrates the leakage of infusedagent into the subarachnoid space via backflow up thecatheter during an actual infusion. A 0.85-mm-diametercatheter was inserted through a bur hole into an in vivo pigbrain to a depth of 14 mm from the cortical surface. A Gd-DTPA and water solution (1:200) was infused at 5 ml/min-ute. A three-dimensional fast spoiled gradient–recalledacquisition MR image (TR 7.8 msec, TE 3.2 msec, ma-trix 256 3 256, field of view 20 cm, slice thickness 1 mm,number of slices 60, number of excitations 2, and flipangle 15˚) was obtained to analyze dispersion of the Gdmarker. Images obtained after 32 minutes of infusionshowed evidence that the infused agent had mostly leakedinto the subarachnoid space, distributing widely along thecontours of the cortex, whereas little distribution into thewhite matter had occurred. These data were obtained from

R. Raghavan, et al.


TABLE 1Phenomena relevant to CED and their determining parameters

Phenomenon Determining Parameters

tissue damage on catheter obviated by catheter design & inser-insertion tion procedure

air bubbles obviated by stylet & catheter design& insertion protocol

backflow along catheter walls poroelastic parameters near catheter:elastic moduli, extracellular vol-ume, & hydraulic conductivity oftissue

fluid flow in extracellular brain hydraulic conductivity of tissue &tissue induced variation of excess pres-

sureefflux rate of water from brain capillary hydraulic conductivity

tissuedrug transport diffusion tensor of drug & convec-

tive velocity drug efflux from tissue capillary molecular permeability–

surface area product drug metabolism, binding, reaction rates& other effects

FIG. 4. a: Schematic depicting two infusion catheters in inhomogeneous tissue (not to scale). The backflow distances,represented by the dark blue cylinders around the catheter tips, vary depending on the hydraulic conductivity of the adja-cent tissue. The backflow length is extended in areas of low conductivity. b: An overlaid T2-weighted MR image dem-onstrating backflow distances (green areas) simulated for two different catheter trajectories (yellow lines). The simulat-ed backflow distances vary significantly within a patient, depending on the chosen trajectory.



an experiment conducted by Michael Bronskill at the Uni-versity of Toronto and funded by BrainLAB AG.

Air Bubbles

Dissolved air and air bubbles are important factors af-fecting the reproducibility and predictability of drug deliv-ery. Significant air bubbles, although not directly a healthhazard, determine the flow along unpredictable paths andare best avoided. Current best practice (which of courseincludes prefilling the catheter) in intraparenchymal de-livery does seem to indicate that air bubbles do not af-fect delivery; nevertheless, predictability may perhaps befurther improved by optimal designs for removing airbubbles (Brady M, Pedain C: US patent submission20040215143, 2004).

White Matter Edema

So far, we have focused on situations in which the back-flow or flow into fluid-filled cavities would almost total-ly compromise infusion. There is, however, another factor

that very significantly affects infusions and must be con-sidered: the increased fluid permeability offered by thewhite matter tracts, which dramatically increases in ede-matous brain tissue. In fact, just infusing fluid into whitematter produces changes that appear very similar to theedema often seen with brain cancers. When infusing intowhite matter that is not already marked by edema, edemaappears around the catheter (Fig. 7).

As can be seen in this figure, relatively little edema ap-pears near the site of tumor recurrence, which lay belowthe resection cavity before infusion. After 44 hours of in-fusion, extensive and intense edema surrounds the cathe-ter. The extent of the edema appears to match the extent ofthe infused fluid closely, according to the infiltration pat-tern of the Gd and SPECT markers. The level of infusion-related edema for a 4.5-ml/minute infusion is often greaterthan that observed in tumor-induced vasogenic edema. OnT2-weighted images, the signal levels near the infusionsite reach levels very near those of fluid-filled cavitiesand ventricles. The infused agent itself may have a high-er signal than that for CSF, so it is difficult to make a



5

FIG. 5. A T1-weighted MR image demonstrating the planned catheter trajectory (bold green line). The thin lines aroundthe planned trajectory represent guidelines designed to indicate the suitability of the trajectory in providing an infusionwithin the interstitial space.

FIG. 6. Four T1-weighted three-dimensional spoiled gradient–recalled acquisition MR images showing the effects ofan infusion of a Gd-DTPA and water solution (1:200). The slice thickness is 3 mm with no gap. The infusion catheter isvisible in the first slice (a). The images reveal leakage and spread of the infused agent into the subarachnoid space.




quantitative assessment from the T2-weighted signals as towhether the infusion-induced edema has a water fractiondifferent from that of the average vasogenic edema. Ei-ther form of edema increases the fraction of extracellularspace, thereby dramatically increasing fluid conductiv-ity along the edematous pathways. This phenomenon canhave a number of repercussions, but the one that concernsus here is the fact that the flow of the infused agent can be-come enslaved to this effect.

Target Heterogeneity

In describing the strong effects of edema, which arelargely confined to white matter on distribution of the in-fused agent, we have implicitly remarked on the inho-mogeneity of the brain tissue, although it is induced by theinfusion. Even in its initial state, however, resistance tofluid flow in brain tissue is both anisotropic (dependent onthe direction of the flow) and heterogeneous (dependenton location within the brain). These two aspects are illus-trated in Fig. 8, which involved both imaging and mathe-matical developments. For the moment, the figures maybe taken as direct representations of the degree of inhomo-geneity variations with location in tissue of the hydraulicconductivity. Because the hydraulic conductivity is reallya symmetric tensor, it is represented by a symmetric ma-trix, which has principal values (or eigenvalues) and prin-cipal axes. So, heterogeneity means that these principalvalues are different in different parts of the brain. In otherwords, the ease of fluid flow is direction-dependent andflow does not occur only in the direction of the pressuregradient. The brightness of the image is a direct map ofthese quantities so that the brightness in Fig. 8a traces theestimated hydraulic conductivity tensor, whereas that inFig. 8b measures the anisotropy of this tensor.

Active Tumors and BBB Disruption

Active tumors present a variety of additional barriersto drug delivery (following extensive pioneering workby Rakesh Jain and his collaborators):12–17 high intersti-tial tumor pressure, decreased vascular surface area with amarkedly more heterogeneous distribution of blood vesselsthan in normal cells, increased intracapillary distances, andperitumoral edema. Most of these factors originate in the

context of a disrupted BBB. The elevated IFP within a tu-mor enhances the rate of drug efflux. Increased IFP alsorestricts the movement of fluid and macromolecules intothe high interstitial pressure regions, as revealed by exper-imental data showing radially outward convection emanat-ing from the tumor. This counteractive convection hindersthe penetration of interstitially delivered therapeutic agentsinto the tumor. Groothuis, et al.,9,10 have demonstrated thatintratumoral drug concentrations in rodents were extreme-ly variable even after CED. In fact, in these studies, CEDfailed to deliver any drug to active tumors. Thus, elevatedIFP is a significant parameter that must be accounted for inexplaining the uneven spatial distribution of therapeuticagents delivered via CED. Although directly administeredmolecules will have much higher initial concentrationsnear the tissue injection site, their rapid clearance and vari-able distribution in the tumor further complicate the devel-opment of an effective drug treatment strategy for highlymalignant tumors. We believe that all the data necessaryto derive patient-specific estimates of these parameters canbe obtained from diffusion tensor and dynamic contrast-enhanced imaging in individual patients, as we will discusslater.

Figure 9 features a schematic of the problem and MRimages visualizing the inefficacy of direct agent deliveryinto a tumor. Focusing on the MR images in Fig. 9, whichwere obtained from Dr. Fred Lang at the MD AndersonCancer Center in Houston, Texas, we see in panel b a stan-dard perfusion image obtained after the intravenous injec-tion of a contrast agent (Gd-DTPA). The presence of thismarker in the tissue signifies disruption and opening of theBBB and is clearly apparent in the figure. Absent otherreasons for BBB disruption, this perfusion pattern is takento be indicative of an active tumor (which in this case wasimplanted in a dog). After sufficient time for this Gd bo-lus to have washed out (as confirmed on imaging), thecontrast agent was administered intraparenchymally via acatheter, which can be seen in outline in Fig. 9c. The cath-eter was inserted directly into the tumor. Interestingly, in-fusion was clearly confined to one side of the tumor andfailed to penetrate the other half. A convincing explana-tion for this result is detailed above; that is, the high intra-tumoral pressures forced the infused agent to one side.

In summary, delivering therapeutic agents directly into

R. Raghavan, et al.


FIG. 7. a: A T2-weighted MR image acquired before the start ofan infusion with two catheters. b: A T2-weighted image of thesame slice 96 hours into the infusion showing increased enhance-ment caused by the infused agent. The added volume leads to anelastic deformation of the brain, which is apparent by a slight mid-line shift and a shift of the resection cavity margins.

FIG. 8. a: Computed diffusion tensor MR image revealing a mapof the trace of the hydraulic conductivity tensor. Bright areas indi-cate regions of high conductivity. b: An MR image demonstrat-ing a map of the anisotropy of the hydraulic conductivity tensor.Bright areas indicate regions with high directionality (anisotropy)of the hydraulic conductivity.




brain parenchyma will revolutionize the treatment of neu-rological disease provided that the process becomes evermore simple, safe, and effective, with continually de-creasing invasiveness across the BBB while remaining intargeted brain regions. Ideally, such a procedure wouldhave the simplicity of an injection but allow targeted andlocalized access to brain tissue. (These features translateimmediately to delivery into other solid tissues, such ashepatomas.) Many people, including us, have shown thatthe brain is not a structure with static constitutive proper-ties for infusions, as illustrated previously. So, for example,infusion of fluids into the brain must allow for changes inthe hydraulic resistance of the brain in response to the infu-sion itself. To reliably account for all factors in planningtherapy for an individual, it would be ideal to have a pa-tient-specific computational model that works. Mathemati-cal and physical modeling of brain physiology sets up gen-eral equations for the distribution of variously deliveredmaterial. The structure of the equations and their solutionsclarifies the requirements for in vivo data that are requiredto predict this distribution and for optimal design of sup-porting devices and delivery methods. We will resumeour discussion of the model construction and imaging de-sign needed after a detour through the topic of device tech-nology.

Delivery Devices: Catheters

We interrupt the conceptual discussion of factors affect-ing agent distribution to discuss some aspects of the deliv-ery devices, specifically, catheters used for CED. (Pumpsfor acute and chronic infusions remain issues, but that isnot the subject of this paper, in part because we have in-sufficient evidence for or against certain points of view.)Early on, catheters used for intraparenchymal deliverywere multiport catheters originally devised for ventricularshunts, for example, for hydrocephalus. An example of oneof the delivery devices used to date is the catheter used inthe Phase II clinical trial of HN-66000, a diphtheria toxinconjugate developed at the NIH. Two catheters (PS Med-ical CSF cardiac/peritoneal catheter; Medtronic, Goleta,CA) with a 2.1-mm outer diameter and 1.2-mm inner di-ameter were stereotactically inserted so that the distal endswere spaced approximately 1 cm apart. We will not discuss

other details of these studies (such as the flow rates, and soforth) given that our focus in this section is the catheters.

The difficulty with CED is in obtaining predictable andadequate flows from all of the catheter’s ports; frequently,fluid flows from the most proximal port. This factor canmake it difficult to control the flow from a linear sequenceof ports placed along the catheter axis, unless the pressurefield inside the catheter is hydrostatic, which is unlike-ly given that most flow impedance occurs in the tissuesthemselves and that there is typically a small but non-neg-ligible gap between the outer wall of the catheter and theparenchymal tissues, serving as a sink for the pressurefield. An example of this phenomenon is shown in Fig. 10:the distribution of dye from an eight-port ventricular cath-eter inserted into gel reveals that flow occurs only fromthe proximal ports. The fundamental cause for this phe-nomenon is not yet known, although we can speculateabout more than one factor that might create a pressuregap across a port that must be breached; once a port is



7

FIG. 9. a: Schematic demonstrating the pressure differential between the extratumoral and the intratumoral interstitialpressures. b: Contrast-enhanced T1-weighted MR image showing a tumor in a dog brain. A catheter was placed throughthe tumor with the tip approximately 1 cm beyond the tumor mass, inside adjacent tissue. c: A T1-weighted MR imageshowing the same slice as that featured in panel b, with Gd-DTPA infused through the catheter. The image reveals thatthe fluid does not suffuse the tumor mass but rather distributes around one side of the catheter and the border of the tumor.

FIG. 10. Digital camera shot depicting infusion of blue dye froman eight-port ventricular catheter inserted into an agarose gel prep-aration. Flow originated only from the most proximal port, render-ing the remaining ports useless for drug delivery.




breached, all flow will occur through that port, leaving thepressure gaps at other ports still intact. Bubbles, viscositydifferences, and other phenomena can account for this. Awell-designed study to isolate the cause would be veryvaluable scientifically but has not, to our knowledge, beenconducted.

Figure 10 shows an infusion of bromophenol blue dyethrough an eight-port ventricular catheter placed in gel.The dye infuses through the most proximal ports only, withno distribution through almost any of the other ports. Thepressure decreases mostly across the most proximal portonly, even in the case of an essentially hydrostatic pressurefield inside the catheter. The same phenomenon has beenobserved during clinical infusions (JH Sampson, et al., un-published data).

Motivated by these deficiencies, we tested several dif-ferent designs to evaluate the volumes of distribution andpressure profiles. The studied devices are shown in Fig.11. The in vitro test procedures and other details, includ-ing results and images of the infusions, were published inthe report by Bauman and colleagues.3 The physical char-acteristics of the catheters are listed in Table 2, includingthe configuration of the portholes and component mate-rials. (Parenthetically, we may remark that the great ad-vantages of this type of in vitro study7 include the relativespeed with which the exploratory infusions can be per-formed and the very low cost of doing such experiments;for example, the agarose gel costs only pennies per sam-ple, in contrast to the vivarium expenses that can accumu-late in in vivo testing. Although in vivo testing of medical

devices like these is an unavoidable necessity before ulti-mately using them in clinical trials in humans, a substan-tial fraction of the expenses can nevertheless be avoidedby following the gel-based approach.)

Representative data demonstrating the volumes of dis-tribution and pressure profiles for each catheter are shownin Figs. 12 (Catheter 1) and 13 (Catheter 2). The dye in-fused into the 0.6% gel was bromophenol blue (molecularweight 690), the flow rate was 5 ml/minute, and the pres-sure was measured in millimeters of Hg. Photos were ob-tained 10 and 40 minutes after the start of the infusion; therun was ended at 40 minutes.

A clear result of these studies was the lack of pre-dictability or uniformity of flow from multiport catheters.Thus, the original ventricular and similar multiport cathe-ters are no longer used for intraparenchymal delivery. Ofcourse, there are several possible solutions to the prob-lem with multiport catheters. One solution, originally per-formed by students at The Johns Hopkins University, is tosignificantly increase resistance within the catheter by in-troducing porous material. This high resistance removesthe sensitivity of the flow to small variations in individualpressure drops across the ports and allows all ports to per-mit fluid flow. Another solution to this problem is to haveseveral separate lumens within one catheter body, witheach lumen feeding its own porthole. This ensures thatthere will be adequate flow from each porthole and, in fact,allows for separate adjustment of each flow rate and/or thesimultaneous infusion of different agents into the targetedtissues.21 A logical extension of any of these strategies is

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FIG. 11. Photograph depicting the different types of catheters tested in the gel experiments. Scale on the left side ofthe image is 1 mm.

TABLE 2Characteristics of catheters evaluated in vitro

Catheter Outer InnerNo. Diameter (mm) Diameter (mm) Material Port Description

A 0.95 0.75 rigid polyamide single, endB 2.5 1.25 flexible silicone single, endC 2.5 1.25 flexible silicone single, laser-cut endD 2.25 1.0 flexible silicone four, radial slitsE 1.75 0.75 clear silicone 3 radial lines of 10 laser-cut holesF 2.0 1.0 barium-impregnated silicone single, endG 2.25 0.75 silicone fishmouth



that of introducing a catheter with controllable portholes.Indeed, specialized injection cannulas with multiple sideports24 and coaxial lumens have been used in trials of celldelivery in humans; the cannula has been withdrawn fromthe brain in time sequences that allow surrounding tissue tohold the implant in place, thus circumventing the refluxproblem.

However, the simplest solution is to use catheters witha single end port. Catheters currently used for infusionare substantially larger than the very thin cannulas, whichhave been characterized as optimal in the rodent brain.Nevertheless, the larger scale of the human brain and thetime allowance after placement of infusion catheters is ex-pected to allow some backflow along the catheter tractwhile maintaining good distribution of the infused agent.

In addition to all of these possibilities, there is anotherbroad class of alternatives that focuses on the active con-trol of the infused agent once it has been pumped from thecatheter(s). We shall not discuss this topic further here. Fi-nally, we should mention that there are several device de-signs that are available or in various stages of develop-ment that aim to minimize backflow.20

Modeling

In Factors Affecting Drug Distribution by CED, we de-

scribed several of the important determinants of the flowof an infused agent continuously injected into the brain.The equations that describe such flow in the idealized sit-uation of a small spherical source and isotropic, homoge-neous tissue have been analyzed by Morrison and col-leagues.27 In Table 3, we display the parameters that arecomputed from the imaging data, whereas Table 4 showsthe validation studies for intermediate variables in thecomputation itself, which are not directly derived fromimage processing. In the present paper, we first briefly re-view the methodology of the mathematical model andthen proceed to the principal imaging methods we cur-rently use and the parameters we expect to obtain fromthese methods. Numerical solutions of the mathematicalmodel27 have been developed,8 and one of us (R.R.) hasproposed patient-specific numerical solutions for eventualclinical use,32,33 which require, of course, patient-specificparameters to obtain the solutions. A more detailed dis-cussion of how these parameters are obtained follows.

Flow Equations

We have been using equations that describe the move-ment of large (usually hydrophilic) molecules in solution;these equations are essentially the same as those featuredin the NIH study.27 These equations allow us to computethe pressure distribution in a rigid porous medium; andthrough the Darcy Law, the interstitial fluid velocity. The



9

FIG. 12. a: Digital camera shot depicting the volume of distribution for Catheter 1 at 10 minutes into the infusion. b:Digital camera shot depicting the volume of distribution for Catheter 1, 40 minutes into the infusion. c: Graph of a pres-sure profile over time (pressure scale in mm Hg), showing a regular, slightly ellipsoid distribution, which is achieved dueto the short backflow distance in conjunction with maintaining the structural integrity of the surrounding gel. The gel trialdoes not reveal issues that would limit the usability of the catheter for CED.

FIG. 13 a: Digital camera shot depicting the volume of distribution for Catheter 2, 10 minutes into the infusion. b:Digital camera shot revealing the volume of distribution for Catheter 2 at 40 minutes into the infusion. c: Graph depict-ing a pressure profile over time (pressure scale in mm Hg), revealing a long backflow distance and a helical disruptionof the gel structure, both indicating the limited suitability of this catheter for use in CED.




equation for the time-dependent concentration of mole-cules can also be solved numerically under general bound-ary conditions. The boundary conditions specify the con-centration at the source of the infusion for the entireduration of the infusion as well as an initial concentration(usually 0) at the start of the computation time. Such prob-lems are called “initial boundary value problems.” Thepoint is that the equations for both pressure and concen-tration have the form of a law of conservation (particles orfluid) together with a proportionality of the fluid or parti-cle current to a force derived from a potential (pressureand concentration gradient). The result is, in either case, aparabolic or elliptical partial differential equation with dif-fusive rather than wave behavior. Note, however, that withnonlinearities in the coefficients, this conclusion does not,in general, hold true.

Software Development

To provide useful solutions for these equations that canbe implemented on neurosurgical workstations, tissue pa-rameters of sufficient accuracy and precision must beextracted from diffusion tensor MR images. The simula-tion produces patient-specific maps of tissue hydraulicconductivity and diffusivity (both are tensor fields), asdescribed later. The application then simulates convec-tion-enhanced infusions in rigid media. Tissue pressureand infusate concentration over time are estimated. Ascreenshot from commercially available software (iPlan!flow application, version 2.0; iplan networks, Buenos Ai-res, Argentina) is shown in Fig. 14.

The simulation output can be visually and quantitativelycompared with experimental results. Studies with pigs areunderway at Virginia Commonwealth University HealthSystem (Richmond, VA) to test these simulations.

We now turn to the imaging methods used in obtainingthe parameters.

Diffusion Tensor Imaging

Diffusion tensor MR imaging with suitable postprocess-ing reveals the self-diffusion tensor coefficients of water inbrain tissue, according to well-known techniques.2 Aftersuitable filtering and correction for motion and distortion,average diffusion coefficients are computed for at least sixindependent gradient directions. A linear system of equa-tions is then solved using these average diffusion coef-ficient values to obtain the six coefficients of the waterself-diffusion tensor at each sample point. Furthermore,cross-property relations between diffusion and other trans-port processes can be used to estimate seemingly unrelatedparameters from the diffusion tensor coefficients. This

method has been used recently to estimate the electricalconductivity tensor.36

One key to utilizing diffusion tensor data is an ability toextract the extracellular diffusion tensor, by which wemean essentially (thought experiment) zeroing out the con-tribution of any intracellular water and any exchange (thatis, the loss of extracellular water to the intracellular com-partment). We have developed an imaging technique toaccomplish this task (unpublished data). Roughly speak-ing, building on the relatively complete model of the MRimaging signal under diffusion-weighted protocols,34 wechoose different magnetic field gradient strengths so thatthe variation in the signals at different gradients is biex-ponential to an excellent approximation, and the exchangecontribution to the signal is negligible. We then obtain justthe extracellular component by comparing normalizedsignals at two such gradient strengths. For this process towork, the diffusion times must be relatively short. We havedeveloped this technique to obtain the hydraulic conduc-tivity tensor, which is key to any simulation involving con-vective transport. We currently estimate three sets of pa-rameters from diffusion tensor imaging data.

Tissue Hydraulic Conductivity, K. The essential ideaused in inferring the tissue hydraulic conductivity, K, isthat the anisotropies of the diffusion tensor give us geo-metric information about the medium, which we can thenuse in inferring the hydraulic conductivity. More pre-cisely, one can develop a formalism for an expansion oftransport functions in terms of point probability functions,which in turn contain all the geometric information aboutthe media. This expansion can be used for the diffusiontensor of water, which is known from MR imaging data,and the probability functions inferred in a least-squaressense at the very least. These estimated probabilities canthen be plugged into the expansion of the hydraulic con-ductivity, which can then be calculated. The basic tech-nique was reported by Tuch and associates,36 and we haveextended the calculation to several levels of approxima-tion of the cluster expansion beyond the least-squares one.Furthermore, there are several other expressions for trans-port coefficients, which may be utilized to derive boundson such cross property values (for example, inferring hy-draulic conductivity, K, from diffusivity, D), and we areexploring these.

Pore Fraction ϕ. As a byproduct of the work involved inobtaining the extracellular diffusion tensor, we can also es-timate the extracellular volume, or pore, fraction ϕ in con-junction with standard MR imaging (M Brady, et al., un-published data). The essential idea again involves choosingthe imaging parameters so that a two-component model,with little exchange, suffices. If we assume that the sig-

R. Raghavan, et al.


TABLE 3Parameters in a model of CED

Parameter Explanation

K tissue hydraulic conductivityϕ resting pore fractionkirr irreversible loss of drug from tissueDM diffusion tensor of drug moleculeLps capillary hydraulic permeability–density productB, G effective bulk & shear moduli of tissue

TABLE 4Intermediate variables in simulations of CED

Variable Explanation

p tissue interstitial pressure during infusionv convective velocity of fluid infusate e, ϕe dilation of tissue, modified pore fraction due to

edemaL backflow distance for prescribed catheter & flow

rate


nal from the intracellular (slow) compartment comes fromwater that remains in that compartment during the diffu-sion time, the intracellular water fraction due to the loss ofsome of the water across the membrane will be underesti-mated. Furthermore, the apparent intracellular water frac-tion is expected to decrease as diffusion time increases, asmore intracellular water will cross the membrane. This re-duction in the intracellular water fraction can be describedby an equation, which can be used as a correction term toimprove the estimate of the extracellular water fraction.

The extracellular water fraction does not directly pro-vide an accurate estimate of the extracellular volume, orpore, fraction ϕ, because water is not uniformly distrib-uted throughout the volume. This is particularly true with-in the white matter, where myelin takes up a significantfraction of the volume but does not contribute much to theMR imaging signal. Assuming that the extracellular fluidcontains a density of water similar to that of CSF, the porefraction ϕ can be estimated by scaling the water fractionby the normalized fraction of water per unit volume, r. Weobtain this variable from a normalized proton density im-age. A region known to be nearly 100% water (the ventri-cles) is selected to normalize this proton density image, sothat the CSF has a r of 1. Multiplying the extracellular wa-ter fraction by r then gives the desired pore fraction ϕ.

Diffusion Tensor for Drug Molecules, DM. The diffusiontensor for drug molecules, DM, diffusing within the extra-cellular fluid can be inferred in exactly the same manneras K. Specifically, the diffusion tensor for a large and ap-proximately spherical molecule can initially be approxi-mated as a scaled extracellular diffusion tensor for the wa-

ter molecule. Of course, we must know the intrinsic valueof the diffusion coefficient of the molecule in an infinitemedium from other sources, but these are generally avail-able. If we do not have ready access to that information,we scale this value according to the size of the molecule.Future developments can include enhancing the theory-based scaling to allow for the shape of the molecule or itsinteractions with the local environment or both (M Brady,et al., unpublished data).

It is well known that the diffusion tensor field can al-so be used to identify fiber pathways, and in fact this ap-plication is now available commercially from BrainLAB,which has licensed the Mori method for commercial use.25

We will further develop this method to identify directionsfor axonal transport.

Dynamic Contrast-Enhanced Imaging

Dynamic contrast-enhanced imaging provides quantita-tive means of obtaining several physical parameters impor-tant in tissues with BBB disruption by following changesin signal intensity from tracer molecules injected into thebloodstream. This imaging modality follows the move-ment of tracer concentrations from the blood vessels intotissue—and back into the vessels, if the measurements areperformed long enough—the signal located principally inregions of BBB disruption. In particular, the permeability-surface area product of the capillaries, local blood flow,and blood volume can be estimated with image postpro-cessing using various models of tracer transport. Thesedata are essential for simulations of transport near tumortissue. The permeability-surface area product, however, is



11

FIG. 14. Screenshot of the iPlan! flow application (version 2) showing the planned trajectories for five catheters andthe results of simulated infusion from these positions.



specific to the tracer molecule used. By varying the sizeof the tracer element, one can develop methods for estimat-ing the permeability of larger molecules. This factor willlead to the assumption, for example, that albumin, suitab-ly attached with a marker such as Gd,31 will behave in itsmovement across the BBB in essentially the same wayas a similarly sized therapeutic molecule, for example, in-terleukin-13 (both are hydrophilic and have molecularweights close to one another, approximately 60,000 D). Ithas been discovered, through microdialysis measurements,that Gd-enhanced regions in brains with active tumor coin-cide with regions of quick ingress and egress of system-ically delivered drugs. Tying Gd to the drug, or a similarlysized, molecule will allow us in a predictable way to com-pute residence time and other quantities of interest—forsystemically administered drugs as well. However, suchtopics are beyond the scope of the present paper.

In summary, we have attempted to describe how onecan obtain patient-specific parameters so that a mathemat-ical model of drug transport via CED can be plugged intosoftware and used by surgeons to plan infusions to obtainthe desired distributions.

Tracking Infused Agents

The final analysis of any infusion model of course liesin the distribution of the particle in question, whether it in-volves a large-molecule protein therapy, a viral carrier ofgene therapy, a cell, or some other particulate. To vali-date such a model, one must ideally be able to measure anagent’s concentration in tissue.22 Leaving aside immuno-histochemical analyses, which involve the killing of ani-mals, we briefly discuss in vivo measurements of concen-trations of molecules and other particles, which may besuitable in human studies.

There is a great advantage in the use of in vivo imagingof drug distributions in humans because it opens the doorto active feedback control of delivery in real time. The im-aging techniques currently available to track fluid distrib-ution provide indirect rather than direct information. Veryrecently, reports have been published on the suitability ofT2-weighted MR images to track agent distribution basedon the drug effects on tissue.23 Other authors have alsoreported on the enhancement of the T2 signal as a conse-quence of fluid administration via CED (J Sampson, et al.,unpublished data). Experiments with nonhuman primatesin which Gd-chelate was coinjected with the drug to mon-itor its distribution have also been performed.22 A num-ber of analyses have been conducted under the direction ofone of the authors of the present paper (J.H.S.), who hastracked surrogate tracers using SPECT studies in whichradioactive iodine-123 conjugated with albumin has beenutilized (unpublished data).

Perhaps new markers for MR imaging can be devel-oped; given the existing knowledge, however, we believethat there is an urgent need for experimentation with thewell-known Gd-chelates, which make excellent markers.(We omit mention of magnetodendrimers simply to limitour discussion. These magnetic tags are not likely to beuseful for molecular agents but rather for cells, and thereare considerable difficulties in quantitative measurementsof concentrations using these agents.) These chelates canbe easily bound or conjugated to various proteins, includ-

ing therapeutic proteins, and should therefore offer, atleast in animal experimentation, direct visualization of aproposed drug. There are several obstacles to overcomebefore this method becomes practical. First, toxicity stud-ies must be performed given that there are few data on thetoxicity of these Gd compounds when they are depositedand reside in brain parenchyma. Nonetheless, it is en-couraging that no toxicity has been displayed within cellcultures; that is, chelates remain stable, so that one canhope to observe the same effects in vivo. Second, Gd isa marker that works by its effects on surrounding watermolecules, and hence is required in relatively large con-centrations to be visible. Thus, for expensive drugs, it maybe a problem to conjugate enough drug molecules fortracking the infused agent. One may need milligrams of aconjugated drug for Gd imaging, whereas the drug mayonly be available in microgram doses. In such cases, onemight have to revert to surrogate tracers, as mentionedearlier.

At the moment, we do not have a definitive solutionfor monitoring drug distribution since each method hassome well-known limitations. For example, in the case ofSPECT, low resolution and variability in the thresholdselection, especially when handling pathological brains,limits accurate tracking of drug distribution and homo-geneity. Monitoring based on a T2 signal is particularlyinefficient when extensive edema or other reasons for T2-signal enhancement are dominant. Positron emission to-mography remains expensive and is still rarely used; inclinical settings, it barely improves on the spatial resolu-tion of SPECT imaging (almost a centimeter in any case).The use of Gd-chelate appears to be a very appropriate sur-rogate marker for tracking fluid distribution, but the safetyof interstitial Gd-chelate for clinical use in human brainsmust still be guaranteed. A coregistration of T2-weightedMR imaging with the results obtained both by tracking thedistribution of an infused drug (both during and after treat-ment) as well as BBB permeability maps obtained usingdynamic contrast-enhanced imaging will play an importantrole in discerning the appropriate explanation for T2 signalvariability.

Optimizing Delivery

We have touched on several factors that affect the dis-position of an agent infused under positive pressure intothe brain parenchyma. Factors that are essentially both un-predictable and manmade, such as tissue coring, introduc-tion of air bubbles, and so forth, are best avoided by usinggood technology. The individuality of the brain, we be-lieve, is validated by good simulations. We have discussedthe hopes we entertain and every step with which such asimulation and its overall validation may be tackled.

Conclusions

In the recitation of the details of the factors affectingCED, we may have lost sight of the fact that a systemsapproach is required; it is essential to develop devicesand simulations together. We hope that, in time, those indrug development take note of all of these advances, andthat the multitude of drugs abandoned by pharmaceuticalcompanies because of the difficulty of delivering theminto brain parenchyma may be reclaimed, and success in

R. Raghavan, et al.



improving therapeutic outcomes realized for brain cancerand other such devastating diseases.

Disclosure

Drs. Pedain, Rodríguez-Ponce, and Hartlep are employed byBrainLAB AG, which has a direct financial interest in the results ofthe authors’ research. The research reported on in this paper hasbeen supported in part by BrainLAB AG, which has a direct finan-cial interest in the results. The other authors have no financial inter-est in the outcomes beyond the support provided by BrainLAB, asmentioned.

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Manuscript received February 1, 2006.Accepted in final form March 16, 2006.This work has been supported in part by NIH Grant No. R44-

NS043105–03 (R.R. and M.L.B.).Address reprint requests to: Raghu Raghavan, Ph.D., Theratax-

is, LLC, 600 Wyndhurst Avenue, Suite 305, Baltimore, Maryland21210-2415. email: [email protected].



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